A class of nonlinear centralizers on nest algebras

Abstract

In order to extend the basic theory of operator algebras, the conditions for a class of nonlinear mappings to become additive centralizers on nest algebras were studied. Firstly, the nest algebras related to a non-trivial nest based on a Hilbert space was defined, and a nonlinear mapping on the nest algebra was defined. Secondly, several properties about this mapping were obtained by using the matrix partitioning method. Finally, it was proved that a nonlinear mapping on the nest algebra that satisfies certain conditions was an additive centralizer, and a specific form for characterizing this mapping was provided. The results show that the nonlinear mapping satisfying some conditions on nested algebras is additive centralizer and can be characterized completely. The research results promote the conclusion that nonlinear mappings become additive centralizers on nested algebras, enrich the classification problem of topological structure for operator algebras, and provide reference and guidance for characterizing other types of nonlinear mappings on nested algebras.

Keywords

• operator algebras; centralizer; nonlinear mapping; hilbert space; matrix partitioning